Stochastic integration with respect to local time of the Brownian sheet and regularising properties of Brownian sheet paths

In this work, we generalise the stochastic local time space integration introduced in (Potential Anal. 13 (2000) 303-328) to the case of Brownian sheet. This allows us to prove a generalised two-parameter Ito formula and derive Davie type inequalities for the Brownian sheet. Such estimates are useful to obtain regularity bounds for some averaging type operators along Brownian sheet curves.